Precalculus Examples

$3 x^{5} - 3 x$ , $9 x^{3} - 9 x$

Step 1

Factor out the GCF of $3 x$ from $3 x^{5} - 3 x + 9 x^{3} - 9 x$ .

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Step 1.1

Factor out the GCF of $3 x$ from each term in the polynomial.

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Step 1.1.1

Factor out the GCF of $3 x$ from the expression $3 x^{5}$ .

$3 x (x^{4}) - 3 x + 9 x^{3} - 9 x$

Step 1.1.2

Factor out the GCF of $3 x$ from the expression $- 3 x$ .

$3 x (x^{4}) + 3 x (- 1) + 9 x^{3} - 9 x$

Step 1.1.3

Factor out the GCF of $3 x$ from the expression $9 x^{3}$ .

$3 x (x^{4}) + 3 x (- 1) + 3 x (3 x^{2}) - 9 x$

Step 1.1.4

Factor out the GCF of $3 x$ from the expression $- 9 x$ .

$3 x (x^{4}) + 3 x (- 1) + 3 x (3 x^{2}) + 3 x (- 3)$

Step 1.2

Since all the terms share a common factor of $3 x$ , it can be factored out of each term.

$3 x (x^{4} - 1 + 3 x^{2} - 3)$

Step 2

The greatest common factor $GCF$ is the term in front of the factored expression.

$3 x$